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1) 针对高维全局优化问题中生物地理学优化算法易陷入局部最优、收敛速度慢的不足，提出一种融合正弦余弦算法和动态混合变异的对偶BBO变体（SCBBO）。该算法首先采用拉丁超立方抽样初始化种群，确保解空间均匀覆盖；其次，在迁移算子中嵌入改进的正弦余弦更新公式，引入非线性递减参数和惯性权重，增强高维环境下的勘探能力；然后，设计动态混合变异算子，结合拉普拉斯变异的大步长探索和高斯变异的精细开发，根据迭代进度自适应调整变异概率，平衡全局与局部搜索；最后，集成对偶学习策略，为每个个体生成对称解，通过比较选择更优者，提升收敛精度。理论分析通过构造数列收敛模型证明算法以概率1全局收敛。在CEC2013高维测试集上的实验表明，SCBBO在1000维至10000维问题上均保持稳定性能，显著优于对比算法。
(2) 为解决复杂多峰优化问题中BBO算法开发能力弱、参数敏感的问题，提出一种基于混合迁移算子和反馈差分进化机制的BBO变体（HFBBO）。该算法引入榜样学习法，在迁移过程中禁止劣解覆盖优解，保留精英信息；混合迁移算子通过随机切换全局迁移（向最优个体学习）和局部迁移（向邻域个体学习），实现搜索模式动态调整；反馈差分进化机制替代传统变异，根据种群多样性指标自动选择差分变异策略（如DE/rand/1或DE/best/2），避免早熟收敛。算法收敛性通过Markov链模型证明，复杂度分析显示其与标准BBO相当。在CEC2014和CEC2017测试集的广泛实验中，HFBBO在多数函数上获得最优结果，Friedman检验排名第一，显示出强大鲁棒性。
(3) 面向现实工程中的约束优化问题，将改进的Oracle惩罚函数法与BBO算法结合，处理等式和不等式约束。该方法将约束违反度转化为自适应惩罚项，动态调整惩罚系数，确保搜索朝向可行域；同时，针对混合变量问题，设计通用离散化处理模块，将离散变量映射为连续编码，优化后再逆映射回原始空间。基于此，开发SCBBO-CH和HFBBO-CH两种算法，应用于CEC2020现实约束优化测试集的57个问题，涵盖机械设计、资源分配等领域。实验结果表明，所提算法在近半数问题上达到理论最优解，且求解效率高于传统罚函数法，验证了其在复杂约束处理中的有效性。
import numpy as np import math def latin_hypercube_sampling(num, dim, bounds): samples = np.zeros((num, dim)) for i in range(dim): segment = (bounds[1] - bounds[0]) / num samples[:, i] = np.array([bounds[0] + (j + np.random.rand()) * segment for j in range(num)]) np.random.shuffle(samples[:, i]) return samples class SCBBO: def __init__(self, num_species, dim, bounds, objective): self.population = latin_hypercube_sampling(num_species, dim, bounds) self.fitness = np.array([objective(ind) for ind in self.population]) self.bounds = bounds self.dim = dim self.best_idx = np.argmin(self.fitness) self.best_solution = self.population[self.best_idx].copy() self.best_fitness = self.fitness[self.best_idx] def migration(self, migration_rates): new_pop = self.population.copy() for i in range(len(self.population)): if np.random.rand() < migration_rates[i]: j = np.random.randint(len(self.population)) for k in range(self.dim): if np.random.rand() < 0.5: new_pop[i][k] = self.population[j][k] return new_pop def sca_update(self, iteration, max_iter): a = 2 - iteration * (2 / max_iter) new_pop = self.population.copy() for i in range(len(self.population)): r1 = a * (1 - iteration / max_iter) r2 = 2 * math.pi * np.random.rand() r3 = 2 * np.random.rand() r4 = np.random.rand() if r4 < 0.5: new_pop[i] += r1 * math.sin(r2) * abs(r3 * self.best_solution - self.population[i]) else: new_pop[i] += r1 * math.cos(r2) * abs(r3 * self.best_solution - self.population[i]) return new_pop def dynamic_mutation(self, iteration, max_iter): mutated = self.population.copy() mutation_prob = 0.1 * (1 - iteration / max_iter) for i in range(len(self.population)): if np.random.rand() < mutation_prob: if np.random.rand() < 0.5: mutated[i] += np.random.laplace(0, 1, self.dim) * 0.5 else: mutated[i] += np.random.normal(0, 1, self.dim) * 0.2 return mutated def dual_learning(self): dual_pop = -self.population.copy() return np.clip(dual_pop, self.bounds[0], self.bounds[1]) def optimize(self, max_iter, objective): for iter in range(max_iter): migration_rates = 1 - (self.fitness - np.min(self.fitness)) / (np.max(self.fitness) - np.min(self.fitness) + 1e-8) self.population = self.migration(migration_rates) self.population = self.sca_update(iter, max_iter) self.population = self.dynamic_mutation(iter, max_iter) dual_pop = self.dual_learning() combined_pop = np.vstack([self.population, dual_pop]) combined_fitness = np.array([objective(ind) for ind in combined_pop]) best_combined_idx = np.argsort(combined_fitness)[:len(self.population)] self.population = combined_pop[best_combined_idx] self.fitness = combined_fitness[best_combined_idx] self.best_idx = np.argmin(self.fitness) if self.fitness[self.best_idx] < self.best_fitness: self.best_fitness = self.fitness[self.best_idx] self.best_solution = self.population[self.best_idx].copy() return self.best_solution, self.best_fitness def ackley_function(x): return -20 * np.exp(-0.2 * np.sqrt(np.mean(x ** 2))) - np.exp(np.mean(np.cos(2 * math.pi * x))) + 20 + math.e scbbo = SCBBO(50, 10, [-32, 32], ackley_function) best_sol, best_fit = scbbo.optimize(100, ackley_function) print(f"Best Solution: {best_sol}, Best Fitness: {best_fit}")如有问题，可以直接沟通
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